{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T13:14:21Z","timestamp":1775913261645,"version":"3.50.1"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2015,1,3]],"date-time":"2015-01-03T00:00:00Z","timestamp":1420243200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2015,8]]},"DOI":"10.1007\/s10898-014-0265-0","type":"journal-article","created":{"date-parts":[[2015,1,2]],"date-time":"2015-01-02T09:06:32Z","timestamp":1420189592000},"page":"763-773","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":37,"title":["Scalarization and pointwise well-posedness for set optimization problems"],"prefix":"10.1007","volume":"62","author":[{"given":"Xian-Jun","family":"Long","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jian-Wen","family":"Peng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zai-Yun","family":"Peng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2015,1,3]]},"reference":[{"key":"265_CR1","volume-title":"Vector Optimization: Set-Valued and Variational Analysis","author":"GY Chen","year":"2005","unstructured":"Chen, G.Y., Huang, X.X., Yang, X.Q.: Vector Optimization: Set-Valued and Variational Analysis. Springer, Berlin (2005)"},{"key":"265_CR2","volume-title":"Variational Methods in Partially Ordered Spaces","author":"A G\u00f6pfert","year":"2003","unstructured":"G\u00f6pfert, A., Riahi, H., Tammer, C., Z\u0103linescu, C.: Variational Methods in Partially Ordered Spaces. Springer, New York (2003)"},{"key":"265_CR3","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-24828-6","volume-title":"Vector Optimization: Theory, Applications, and Extensions","author":"J Jahn","year":"2004","unstructured":"Jahn, J.: Vector Optimization: Theory, Applications, and Extensions. Springer, Berlin (2004)"},{"key":"265_CR4","volume-title":"Theory of Vector Optimization. Lecture Notes in Economics and Mathematics Systems","author":"DT Luc","year":"1989","unstructured":"Luc, D.T.: Theory of Vector Optimization. Lecture Notes in Economics and Mathematics Systems, vol. 319. Springer, New York (1989)"},{"key":"265_CR5","unstructured":"Kuroiwa, D.: Some duality theorems of set-valued optimization with natural critera. In: Proceedings of the International Conference on Nonlinear Analysis and Convex Analysis, pp. 221\u2013228. World Scientific, River Edge (1999)"},{"key":"265_CR6","doi-asserted-by":"crossref","first-page":"1935","DOI":"10.1016\/S0362-546X(01)00274-7","volume":"47","author":"D Kuroiwa","year":"2001","unstructured":"Kuroiwa, D.: On set-valued optimization. Nonlinear Anal. 47, 1935\u20131400 (2001)","journal-title":"Nonlinear Anal."},{"key":"265_CR7","first-page":"73","volume":"24","author":"D Kuroiwa","year":"2003","unstructured":"Kuroiwa, D.: Existence theorems of set optimization with set-valued maps. J. Inf. Optim. Sci. 24, 73\u201384 (2003)","journal-title":"J. Inf. Optim. Sci."},{"key":"265_CR8","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1007\/s10957-004-6472-y","volume":"124","author":"TXD Ha","year":"2005","unstructured":"Ha, T.X.D.: Some variants of the Ekeland variational principle for a set-valued map. J. Optim. Theory Appl. 124, 187\u2013206 (2005)","journal-title":"J. Optim. Theory Appl."},{"key":"265_CR9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jmaa.2006.01.033","volume":"325","author":"E Hern\u00e1ndez","year":"2007","unstructured":"Hern\u00e1ndez, E., Rodr\u00edguez-Mar\u00edn, L.: Nonconvex scalarization in set optimization with setvaled maps. J. Math. Anal. Appl. 325, 1\u201318 (2007)","journal-title":"J. Math. Anal. Appl."},{"key":"265_CR10","doi-asserted-by":"crossref","first-page":"1276","DOI":"10.1016\/j.na.2006.08.013","volume":"67","author":"E Hern\u00e1ndez","year":"2007","unstructured":"Hern\u00e1ndez, E., Rodr\u00edguez-Mar\u00edn, L.: Existence theorems for set optimization problems. Nonlinear Anal. 67, 1276\u20131736 (2007)","journal-title":"Nonlinear Anal."},{"key":"265_CR11","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1007\/s10957-010-9752-8","volume":"148","author":"J Jahn","year":"2011","unstructured":"Jahn, J., Ha, T.X.D.: New order relations in set optimization. J. Optim. Theory Appl. 148, 209\u2013236 (2011)","journal-title":"J. Optim. Theory Appl."},{"key":"265_CR12","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1007\/978-3-642-46618-2_2","volume-title":"Recent Advances and Historical Development of Vector Optimiation Problems. Lecture Notes in Economics and Mathematical Systems","author":"EM Bednarczuck","year":"1987","unstructured":"Bednarczuck, E.M.: Well posedness of vector optimization problem. In: Jahn, J., Krabs, W. (eds.) Recent Advances and Historical Development of Vector Optimiation Problems. Lecture Notes in Economics and Mathematical Systems, vol. 294, pp. 51\u201361. Springer, Berlin (1987)"},{"key":"265_CR13","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1007\/s11228-011-0182-z","volume":"19","author":"EM Bednarczuck","year":"2011","unstructured":"Bednarczuck, E.M., Miglierina, E., Molho, E.: A mountain pass-type theorem for vector-valued functions. Set-Valued Var Anal. 19, 569\u2013587 (2011)","journal-title":"Set-Valued Var Anal."},{"key":"265_CR14","doi-asserted-by":"crossref","first-page":"3821","DOI":"10.1016\/j.na.2012.02.004","volume":"75","author":"Y Araya","year":"2012","unstructured":"Araya, Y.: Four types of nonlinear scalarizations and some applications in set optimization. Nonlinear Anal. 75, 3821\u20133835 (2012)","journal-title":"Nonlinear Anal."},{"key":"265_CR15","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/0041-5553(66)90003-6","volume":"6","author":"AN Tykhonov","year":"1966","unstructured":"Tykhonov, A.N.: On the stability of the functional optimization problems. USSR Comput. Math. Phys. 6, 28\u201333 (1966)","journal-title":"USSR Comput. Math. Phys."},{"key":"265_CR16","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0084195","volume-title":"Well-Posed Optimization Problems. Lecture Notes in Mathematics","author":"AL Dontchev","year":"1993","unstructured":"Dontchev, A.L., Zolezzi, T.: Well-Posed Optimization Problems. Lecture Notes in Mathematics, vol. 1543. Springer, Berlin (1993)"},{"key":"265_CR17","first-page":"107","volume":"23","author":"EM Bednarczuck","year":"1994","unstructured":"Bednarczuck, E.M.: An approach to well-posedness in vector optimization: consequences to stability and parametric optimization. Control Cybern. 23, 107\u2013122 (1994)","journal-title":"Control Cybern."},{"key":"265_CR18","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/BF02192533","volume":"89","author":"D Dentcheva","year":"1996","unstructured":"Dentcheva, D., Helbig, S.: On variational principles, level sets, well-posedness and $$\\varepsilon $$ \u03b5 -solutions in vector optimization. J. Optim. Theory Appl. 89, 325\u2013349 (1996)","journal-title":"J. Optim. Theory Appl."},{"key":"265_CR19","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1007\/s10957-007-9272-3","volume":"135","author":"YP Fang","year":"2007","unstructured":"Fang, Y.P., Hu, R., Huang, N.J.: Extended $$B$$ B -well-posedness and Property (H) for set-valued vector optimization with convexity. J. Optim. Theory Appl. 135, 445\u2013458 (2007)","journal-title":"J. Optim. Theory Appl."},{"key":"265_CR20","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1007\/BF00927717","volume":"5","author":"M Furi","year":"1970","unstructured":"Furi, M., Vignoli, A.: About well-posed minimization problems for functionals in metric spaces. J. Optim. Theory Appl. 5, 225\u2013229 (1970)","journal-title":"J. Optim. Theory Appl."},{"key":"265_CR21","first-page":"171","volume-title":"Recent Developments in Cariational Well-posedness Probems. Mathematics and Its Applications","author":"P Loridan","year":"1995","unstructured":"Loridan, P.: Well-posedness in vector optimization. In: Lucchetti, R., Recalski, J. (eds.) Recent Developments in Cariational Well-posedness Probems. Mathematics and Its Applications, vol. 331, pp. 171\u2013192. Kluwer, Dordrecht (1995)"},{"key":"265_CR22","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1007\/s001860300310","volume":"58","author":"E Miglierina","year":"2003","unstructured":"Miglierina, E., Molho, E.: Well-posedness and convexity in vector optimization. Math. Methods Oper. Res. 58, 375\u2013385 (2003)","journal-title":"Math. Methods Oper. Res."},{"key":"265_CR23","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1023\/A:1017595610700","volume":"108","author":"XX Huang","year":"2001","unstructured":"Huang, X.X.: Pointwise well-posedness of perturbed vector optimization problems in a vector-valued variational principle. J. Optim. Theory Appl. 108, 671\u2013687 (2001)","journal-title":"J. Optim. Theory Appl."},{"key":"265_CR24","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1007\/s10957-005-4723-1","volume":"126","author":"E Miglierina","year":"2005","unstructured":"Miglierina, E., Molho, E., Rocca, M.: Well-posedness and scalarization in vector optimization. J. Optim. Theory Appl. 126, 391\u2013409 (2005)","journal-title":"J. Optim. Theory Appl."},{"key":"265_CR25","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1007\/s00186-007-0162-0","volume":"66","author":"M Durea","year":"2007","unstructured":"Durea, M.: Scalarization for pointwise well-posedness vectorial problems. Math. Methods Oper. Res. 66, 409\u2013418 (2007)","journal-title":"Math. Methods Oper. Res."},{"key":"265_CR26","first-page":"3768","volume":"71","author":"WY Zhang","year":"2008","unstructured":"Zhang, W.Y., Li, S.J., Teo, K.L.: Well-posedness for set optimization problems. Nonlinear Anal. 71, 3768\u20133788 (2008)","journal-title":"Nonlinear Anal."},{"key":"265_CR27","doi-asserted-by":"crossref","first-page":"1822","DOI":"10.1016\/j.na.2011.09.028","volume":"75","author":"C Guti\u00e9rrez","year":"2012","unstructured":"Guti\u00e9rrez, C., Miglierina, E., Molho, E., Novo, V.: Pointwise well-posedness in set optimization with cone proper sets. Nonlinear Anal. 75, 1822\u20131833 (2012)","journal-title":"Nonlinear Anal."},{"key":"265_CR28","doi-asserted-by":"crossref","first-page":"612","DOI":"10.1007\/s10957-012-0205-4","volume":"157","author":"XJ Long","year":"2013","unstructured":"Long, X.J., Peng, J.W.: Generalized $$B$$ B -well-posedness for set optimization problems. J. Optim. Theory Appl. 157, 612\u2013623 (2013)","journal-title":"J. Optim. Theory Appl."},{"key":"265_CR29","volume-title":"Topology, vols. 1 and 2","author":"K Kuratowski","year":"1968","unstructured":"Kuratowski, K.: Topology, vols. 1 and 2. Academic Press, New York (1968)"},{"key":"265_CR30","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/BF00940478","volume":"67","author":"C Gerth","year":"1990","unstructured":"Gerth, C., Weidner, P.: Nonconvex separation theorems and some applications in vector optimization. J. Optim. Theory Appl. 67, 297\u2013320 (1990)","journal-title":"J. Optim. Theory Appl."}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-014-0265-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-014-0265-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-014-0265-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T04:59:08Z","timestamp":1559278748000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-014-0265-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1,3]]},"references-count":30,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2015,8]]}},"alternative-id":["265"],"URL":"https:\/\/doi.org\/10.1007\/s10898-014-0265-0","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,1,3]]}}}